Quantum instanton approach to metastable collective spin systems: Numerical implementation and applications

summary

Video file (mp4)

The gist

The gist Driven-dissipative collective spin systems can host several long-lived metastable states; rare switching between them governs slow relaxation and first-order dissipative phase transitions

In short

The paper introduces a quantum instanton framework using exact quasiprobability dynamics to describe rare switching between long-lived metastable states in driven-dissipative collective spin systems. This method was numerically implemented and applied to the Lipkin-Meshkov-Glick and cooperative resonance fluorescence models, successfully predicting stationary magnetization, phase transition points, and relaxation rate scaling.

Key concepts

Driven-dissipative collective spin systems
These are physical systems where a collective set of spins is influenced by both external driving forces (like an applied field) and dissipation (energy loss to the environment). They can get stuck in several long-lived states, and switching between these states is key to understanding slow relaxation.
Quantum instanton framework
This mathematical tool uses the dynamics of a specific quasiprobability distribution to calculate activation barriers. By finding 'instanton trajectories'—paths that minimize action—researchers can determine the probability and rate at which the system switches between different metastable states.
Quasiprobability representation
This refers to a mathematical way of describing the system's state using a distribution $p_ ho$. The choice of this representation, such as collocation or Wigner, impacts how accurately the instanton trajectories are calculated. The paper shows that different choices yield varying numerical accuracy.
First-order dissipative phase transitions
These are sharp changes in the system's dominant stationary state that occur when a certain parameter is crossed. In these systems, this transition is governed by the rare switching between metastable states, which the instanton method helps locate.

Terminology used across episodes

This episode discusses

The paper

Quantum instanton approach to metastable collective spin systems: Numerical implementation and applications · Read on arXiv

Maciej Chudak, Massimiliano Esposito, Krzysztof Ptaszyłnski

Institute of Molecular Physics, Polish Academy of Sciences · University of Luxembourg

Driven-dissipative collective spin systems can host several long-lived metastable states; rare switching between them governs slow relaxation and first-order dissipative phase transitions associated with changes in the dominant stationary state. In the companion Letter [arXiv:2604.15091], we introduced a quantum instanton framework based on exact quasiprobability dynamics to describe this switching and illustrated it with a minimal model possessing a simplifying symmetry. Here we develop its numerical implementation, combining collocation and shooting methods, and apply it to two microscopically motivated systems: the Lipkin-Meshkov-Glick model with purely collective dissipation and the cooperative resonance fluorescence with collective and local dissipation. By determining the leading exponential scaling of switching rates between metastable attractors, we predict the stationary magnetization, the first-order dissipative phase-transition point, and the exponential scaling of slow relaxation rates. These predictions agree with quantum master-equation calculations and an exact analytical result for the second model without dephasing. We also examine how the choice of quasiprobability representation affects numerical convergence and find that the alternative semiclassical Wigner approach, based on Gaussian truncation, has varying accuracy across models and parameter regimes. These results substantiate the framework's applicability to experimentally relevant collective spin systems with both collective and local dissipation.

Transcript

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Quantum instanton approach to metastable collective spin systems".

Mira: The gist Driven-dissipative collective spin systems can host several long-lived metastable states;

Kai: First, who's behind it and why it matters.

Paper summary: Kai: So we're moving on to summarizing this paper again. The main thesis is that in driven-dissipative collective spin systems, you have these long-lived metastable states, and the rare switching between them dictates both the slow relaxation and those first-order dissipative phase transitions that happen when the dominant stationary state shifts.

Mira: Exactly. They claim that their quantum instanton framework allows them to describe this switching using exact quasiprobability dynamics, and they’ve shown it works by illustrating it with a minimal model that has some simplifying symmetry.

Lev: The point is they develop the numerical implementation themselves, combining collocation and shooting methods to approximate those instanton segments where pi is not zero by a finite time trajectory with boundary conditions approximating the exact asymptotic ones.

Kai: And they apply this to two systems: the Lipkin–Meshkov–Glick model with purely collective dissipation, and cooperative resonance fluorescence with both collective and local dissipation.

Mira: The overall goal is that by determining the leading exponential scaling of those switching rates between metastable attractors, they can predict the stationary magnetization, the first-order dissipative phase-transition point, and how fast those slow relaxation rates scale exponentially.

Lev: And they found that their predictions for these quantities agree with quantum master equation calculations and also with an exact analytical result for the second model without dephasing.

Kai: It matters because it shows that this framework is applicable to experimental systems involving both collective and local dissipation, which is a key feature in many real-world collective spin setups.

Mira: So, the paper sets up the connection between the quantum dynamics of these systems and observable macroscopic phenomena like relaxation times and transition points.

Lev: It’s about taking those complicated quantum descriptions of switching and turning them into something you can actually use to predict how a physical system will behave when it's being driven or dissipated.

Conclusion: Kai: Looking at the full title, "Quantum instanton approach to metastable collective spin systems: Numerical implementation and applications," it tells you exactly what this paper is about—it’s about using a quantum instanton method to study these specific types of driven-dissipative systems.

Mira: It emphasizes that they didn't just stop at the theory, but they developed the numerical implementation themselves and tested it on real physical models, which really grounds the work in something tangible.

Lev: For someone working with hardware, it tells you that this is a tool you can potentially use to model systems where you need to understand how rare transitions affect system dynamics on your actual devices.

Kai: In simple terms, what they're saying is that rare events in these spin systems determine the entire long-term behavior of the system, and this paper gives us a way to calculate those rare event rates accurately.

Mira: It’s about linking the quantum world of instanton trajectories to observable things like how long it takes for a physical system to settle into its final state or where a phase transition occurs.

Lev: So, the implication is that if you have such systems in your lab, this framework gives you a way to calculate those critical rates without needing an impossibly complex analytical solution every single time.

More episodes

← Home